[list][*]Subject: Mathematics[br][/*][*]Grade: 9th grade [br][/*][*]Duration: 50 min [br][/*][*]ICT tools: [i]computer teacher projector, computers for students, or tablets / phones.[/i][i] [/i][i][/i][/*][/list]

[i]This lesson is about monotony and sign of linear function.[/i]

[i]At the end of the lesson, students should know:[/i][list][*][i]to analyze and determine the monotony of a given linear function;[/i][/*][*][i]to analyze and determine the sign of a given linear function.[/i][/*][/list]

[i]By the end of the lesson, students should know:[/i][list][*][i]to determine points of intersection between graph and coordinates axes and to to represent a linear function;[/i][/*][*][i]characterize the monotony and sign by the help of graphic reading;[/i][/*][*][i]to determine the sign of a linear function with given coefficients;[/i][/*][*][i]to determine linear functions monotony with known dominant coefficient.[/i][/*][/list]

[i][b][i]Methods and teaching:[/i][/b] [br]Heuristic conversation, guided discovery, mathematical modeling, logical argument. [br][br][i][b]The times of the lesson:[br][br][/b][/i][u] I) Class organization and Introduction (2 min.)[br][/u] The teacher shows the subject of the lesson: study of some properties of the linear functions by reading of graphics, with worksheets classical books, but also on computers, using two sheets Interactive GeoGebra. Students will receive printed sheets and all students will have access to interactive files.[br][br][u]II) Verification of prior knowledge (12 min.)[br][/u]Students solve Worksheet 1. Questions: - How do we find the intersection between graph of a linear function and axes? - What we can see about monotony of function, but about the sign? - If you change the coefficient (in interactive sheet 1), what happens with the sign, but about the monotony?[br] [br][u]III) Learning of new knowledge (20 min.)[br][/u]Students study the graph for more values ​​of coefficients a and b. They discuss and draw conclusions, then check with interactive sheet 2 and the conclusions are written on notebooks. We ensure they have enough time to understand the behavior of linear functions and depending on the coefficient a. Questions: - How does the graph for a = 0? - it is a horizontal straight line y = b (constant); - What equation has a vertical right? - x = c (constant) How can we record these results for a specific feature? The teacher draws on the blackboard a sign table, helping students to synthesize results and acquire a mnemonic scheme. Students draw sign tables for functions already studied, then get the next task. Students solve Worksheet 2 individually or in teams, with the help of the teacher. Questions / tasks: - What is a logical argument? (Sheet 2 exercise 1) - Let make statements (hypothesis and conclusion) based on reading charts, then let prove them. (Sheet 2 exercise 2) - What happens to the inequality when multiplied by a negative number?[br][br][u]IV) Deepening and evaluation (13 min.)[br][/u] Students will solve inequalities of Sheet 2 Exercise 3, possibly receiving instructions on how to use a sign table to solve inequalities. Check all with interactive sheets (GeoGebra).[br][br][i][u]IV) Transferring (3 min.)[/u][/i] [br]Students [i]receive as a theme for the home a selection of exercises and problems from textbook.[br][/i] [/i][br]

[i]Printable sheets:[br][list][*][i] [url=https://ggbm.at/MWKqerbX]https://ggbm.at/MWKqerbX[/url][/i][br][/*][/list]Interactive work sheets:[br][list][*][i]"Linear function graph" [url=https://ggbm.at/d3mWUWfC]https://ggbm.at/d3mWUWfC[/url][/i][br][/*][*][i]"The monotony and sign of linear function" [url=https://ggbm.at/x9sEWe4h]https://ggbm.at/x9sEWe4h[/url][/i][/*][/list][/i]

[i][i][list][*]We will use GeoGebra for graphics manipulation and detection of the intrinsic properties of the linear function and the way in which the coefficients affect the graphical representation.[/*][*]material will be prepared for the event of absence of the Internet and download / stream.[br][/*][*]possibly students will study site GeoGebra before the lesson, to accommodate with platform and will find that the software is available on mobile.[/*][/list][/i][/i]